A153887 Smallest of five consecutive Fibonacci numbers whose sum is a prime number.

0, 1, 2, 8, 89, 144, 2584, 121393, 196418, 832040, 20365011074, 4052739537881, 8944394323791464, 99194853094755497, 2880067194370816120, 14028366653498915298923761, 96151855463018422468774568

Offset

1,3

Comments

0+1+1+2=3=7, 1+2+3+5+8=19, 2+3+5+8=13=31, 8+13+21+34+55=131, 89+144+233+377+610=1453, 144+233+377+610+987=2351,...

Links

Table of n, a(n) for n=1..17.

Formula

For n>=3, a(n) + A000032(m+4) is prime, where m is the Fibonacci index of a(n) (see example). This follows from the identity F(m+1) + F(m+2) + F(m+3) + F(m+4) = A000032(m+4), m>=0. - Vladimir Shevelev, Apr 24 2014

Example

For n=3,4, the Fibonacci indices of a(3)=2, a(4)=8, are 3,6 respectively. So a(3) + A000032(7)= 31,  a(4) + A000032(10) = 131. - Vladimir Shevelev, Apr 24 2014

Mathematica

a=0; b=1; c=1; d=2; lst={}; Do[e=Fibonacci[n]; p=a+b+c+d+e; If[PrimeQ[p], AppendTo[lst, a]]; a=b; b=c; c=d; d=e, {n, 4, 6!}]; lst
Select[Partition[Fibonacci[Range[1000]], 5, 1], PrimeQ[Total[#]]&][[All, 1]] (* Harvey P. Dale, Dec 01 2016 *)

Crossrefs

Cf. A000045, A001906, A000071, A001605, A153862, A153863, A153865, A153866, A153867.

Sequence in context: A012295 A009486 A110384 * A131349 A319124 A294194

Adjacent sequences: A153884 A153885 A153886 * A153888 A153889 A153890

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Status

approved